$\dfrac{ 4v + 4w }{ -6 } = \dfrac{ 10v - 9x }{ -2 }$ Solve for $v$.
Multiply both sides by the left denominator. $\dfrac{ 4v + 4w }{ -{6} } = \dfrac{ 10v - 9x }{ -2 }$ $-{6} \cdot \dfrac{ 4v + 4w }{ -{6} } = -{6} \cdot \dfrac{ 10v - 9x }{ -2 }$ $4v + 4w = -{6} \cdot \dfrac { 10v - 9x }{ -2 }$ Reduce the right side. $4v + 4w = -{6} \cdot \dfrac{ 10v - 9x }{ -{2} }$ $4v + 4w = {3} \cdot \left( 10v - 9x \right)$ Distribute the right side $4v + 4w = {3} \cdot \left( {10v} - {9x} \right)$ $4v + 4w = {30}v - {27}x$ Combine $v$ terms on the left. ${4v} + 4w = {30v} - 27x$ $-{26v} + 4w = -27x$ Move the $w$ term to the right. $-26v + {4w} = -27x$ $-26v = -27x - {4w}$ Isolate $v$ by dividing both sides by its coefficient. $-{26}v = -27x - 4w$ $v = \dfrac{ -27x - 4w }{ -{26} }$ Swap signs so the denominator isn't negative. $v = \dfrac{ {27}x + {4}w }{ {26} }$